Intricately Intertwined

In a chapter on symmetry, it was casually mentioned that graphs have not thickness. Of course they don’t but I had never thought about it. In fact, images of parabolas and circles are all wrong because they have a form of line. In reality, they can not have a line but only an infinite number of points that form a curve.

This translated into a thought that stemmed from the book on Cezanne that I recently finished reading. He realized that although people usually begin to draw a ball by first drawing a circle, the actual object has no line at all. So how do I know that the ball exists, and that it is separated from the room around it? It is because of the changes in color, and value. These changes result from the varying surfaces and their reflections of light due to their different curvatures. Everything consists of surfaces, and those surfaces have varying curvatures.

So now we have wrapped back around to mathematics. Different surfaces can be described by a piece of paper and a stick of charcoal. They can also be described by mathematics. Many people think my love of both mathematics and art is an odd combination; but my mind doesn’t. To me they are completely integrated, with their concepts intricately intertwined.